The Sound Of Inevitability

Sunday, 21 December 2014

By Dara O'Kearney

A while back, Pablo Gordillo, a Spanish pro living in the United Kingdom, pulled off an almost unbelievable hat-trick. He overcame three huge fields in the Sunday Kick Off, the Sunday Storm and The Bigger $55 tournaments in one day on PokerStars, to earn a combined sum of $101,060. The reaction to this feat was interesting but predictable; rather than celebrating this remarkable success, much of the community centred on how the supposedly astronomical odds of this happening (one in 348,455,720,808 was the number armchair mathematicians arrived at simply by multiplying together the different field sizes) indicated that it couldn't just happen by chance. The "Online is rigged!" conspiracy theorists kicked into overdrive. Their argument was simple - how could something that is almost 350 billion to one to happen actually occur otherwise?

Before examining the dubious assumptions underlying this figure, allow me to point out that the human mind doesn't intuitively handle probability (much less improbability) very well. Lottery organisers know this; that's why to win the highest prize in the EuroMillions, all you have to do is pick the five numbers from one to fifty that rise up out of one drum, and both numbers between one and eleven plucked from another. The odds of successfully doing this are one in 116,531,800. So if the organisers simply got everyone to pick a number between 1 and 116,531,800 it would be the same thing, right? In terms of odds, yes, but in terms of public perception of its improbability, not at all. Most people, when told that they would only win if their specific number between one and 116,531,800 gets selected would, quite rightly, feel this was incredibly unlikely. By contrast, most of us imagine that picking the correct five numbers from fifty, followed by two from eleven feels much more likely to be achievable. In reality, the odds are identical.

Now let's imagine a hypothetical 'Billionaire' Lottery. Everybody on the planet is given a lottery ticket every week for a year. There's only one prize - a billion dollars. But it will be won at some point during the year, guaranteed. What happens when someone eventually does win? The winner celebrates his or her astounding fortune and it is acknowledged that they are the luckiest person on the planet. But I'm pretty sure there wouldn't be the same cries of “Rigged!" that we got after Gordillo's trifecta. Why not? There are 7.125 billion people on the planet, give or take a few. 7.125 billion multiplied by fifty-two weeks (the number of tickets issued in our hypothetical lottery) is actually a bigger number than 350 billion to one, the supposed odds on Gordillo's treble. So why does what is almost a 350 billion to one shot coming in immediately draw derisory accusations of an uneven playing field while another even less probable outcome wouldn't?

It is because of the way the human brain processes improbability.The odds of anyone winning a lottery are huge, but one ticket will win it, so we focus on the inevitability. When an equally improbable event is not guaranteed to happen but then does, we focus on the improbability.

Now let's look at some of the assumptions underlying the original 'single' chance in 348,455,720,808 calculation that Gordillo would see that winning banner pop up three times. Since this number is arrived at simply by multiplying the three field sizes together, that statistic assumes that a poker tournament is a lottery where everyone has an equal chance of winning. This is, of course, nonsense. We all know poker has a skill component as well as luck, and that the best players therefore have a much better chance of success than the worst. To quantify the degree to which this is true, I examined the online win rate of several of the top MTT players in the world in Sunday fields with 1,000 runners or more. A quick look at their statistics suggest that the better pros win about ten times more often than average. In other words, in a 35,000 runner field like the Sunday Storm, the best players have approximately one chance in 3500 of winning, and the worst players might be million to one shots to balance this out. If Gordillo belongs in this upper echelon, (and given that he's a pro and has already final tabled two EPTs in his short career, that seems like a reasonable assumption), suddenly the odds of his trifecta shrink from 350 billion down to 350 million to one. Still highly improbable, but now only about three times as unlikely as winning the EuroMillions jackpot.

Can we apply some of the improbable but inevitable logic of lotteries here? Yes, we can. Someone has to win the Sunday Storm. If that person is a top class player with ten times the average chance of winning any given tournament, and they also enter the Sunday Kick Off and The Bigger 55, then the chances they ship those two are less than 100,000 to 1. About the same odds as someone winning three ten-man SnGs in a row, something most people would agree to be unlikely, but not incredible or impossible.

It's also worth pointing out that the reason we are talking about these specific three tournaments, the Sunday Kick Off, the Sunday Storm and The Bigger $55. We're discussing those ones because, out of the hundred or so tournaments he played that day, those are the three he happened to win. Had he won the Sunday Warm Up, the Sunday Million and The Bigger 109 too, the armchair mathematicians would no doubt have multiplied those three field sizes together to give us an even more improbable statistic. Thank goodness Gordillo bricked those.

If the true odds of any top class player pulling off this particular treble are around 100,000 to one, then you factor in all the other possible combinations of tournament triplets that could be won by the same player, as well as the many hundreds of top class players flicking it in to up to a hundred big runner Sunday fields, then the odds of this happening at some point shrink to the point where it is almost inevitable it would have happened. So, far from Gordillo's achievement being the seemingly impossible occurrence the conspiracy theorists and armchair mathematicians proclaimed, it was simply a case that someone's numbers were bound to come up sooner or later.

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